{"id":255502,"date":"2025-07-13T05:34:10","date_gmt":"2025-07-13T05:34:10","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=255502"},"modified":"2025-07-13T05:34:12","modified_gmt":"2025-07-13T05:34:12","slug":"convert-110-degrees-to-radians-using-the-ratio","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/13\/convert-110-degrees-to-radians-using-the-ratio\/","title":{"rendered":"Convert 110 degrees to radians using the ratio"},"content":{"rendered":"\n<p>Convert 110 degrees to radians using the ratio \\frac{?}{180}<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-0-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>To convert degrees to radians, you can use the following formula: radians=degrees\u00d7\u03c0180\\text{radians} = \\text{degrees} \\times \\frac{\\pi}{180}radians=degrees\u00d7180\u03c0\u200b<\/p>\n\n\n\n<p>In this case, to convert 110 degrees to radians: 110\u2009degrees\u00d7\u03c0180110 \\, \\text{degrees} \\times \\frac{\\pi}{180}110degrees\u00d7180\u03c0\u200b<\/p>\n\n\n\n<p>Now, simplify the multiplication: 110\u00d7\u03c0180=110\u03c0180110 \\times \\frac{\\pi}{180} = \\frac{110\\pi}{180}110\u00d7180\u03c0\u200b=180110\u03c0\u200b<\/p>\n\n\n\n<p>We can simplify the fraction 110180\\frac{110}{180}180110\u200b by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 10: 110180=1118\\frac{110}{180} = \\frac{11}{18}180110\u200b=1811\u200b<\/p>\n\n\n\n<p>So, the equation becomes: 11\u03c018\\frac{11\\pi}{18}1811\u03c0\u200b<\/p>\n\n\n\n<p>Thus, 110 degrees is equivalent to: 11\u03c018\u2009radians\\frac{11\\pi}{18} \\, \\text{radians}1811\u03c0\u200bradians<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation:<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Degrees to Radians Conversion<\/strong>: The relationship between degrees and radians is defined by the fact that a full circle is 360\u2218360^\\circ360\u2218 or 2\u03c02\\pi2\u03c0 radians. Therefore, the conversion factor is \u03c0180\\frac{\\pi}{180}180\u03c0\u200b, meaning for every degree, you multiply by \u03c0180\\frac{\\pi}{180}180\u03c0\u200b to get the equivalent radians.<\/li>\n\n\n\n<li><strong>Simplification<\/strong>: When converting, it&#8217;s often necessary to simplify the fraction to its lowest terms. In this case, we divided both 110 and 180 by their GCD, which was 10, to make the expression simpler.<\/li>\n<\/ul>\n\n\n\n<p>Thus, the radian measure of 110 degrees is 11\u03c018\\frac{11\\pi}{18}1811\u03c0\u200b radians<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner6-452.jpeg\" alt=\"\" class=\"wp-image-255503\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Convert 110 degrees to radians using the ratio \\frac{?}{180} The Correct Answer and Explanation is: To convert degrees to radians, you can use the following formula: radians=degrees\u00d7\u03c0180\\text{radians} = \\text{degrees} \\times \\frac{\\pi}{180}radians=degrees\u00d7180\u03c0\u200b In this case, to convert 110 degrees to radians: 110\u2009degrees\u00d7\u03c0180110 \\, \\text{degrees} \\times \\frac{\\pi}{180}110degrees\u00d7180\u03c0\u200b Now, simplify the multiplication: 110\u00d7\u03c0180=110\u03c0180110 \\times \\frac{\\pi}{180} = \\frac{110\\pi}{180}110\u00d7180\u03c0\u200b=180110\u03c0\u200b We [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center 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